Energy to put space shuttle in orbit

In summary, the conversation revolves around calculating the energy needed to put a space shuttle into orbit, with a given circular orbit height and mass of the shuttle and Earth. The equation used is KE=GMm/rp, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the shuttle, and rp is the distance between the Earth's surface and the orbit height. The final answer should be 2.2*10^12J, which is the total energy needed for the shuttle to be in orbit.
  • #1
calculator20
47
0

Homework Statement


The space shuttle orbits about 300km above the surface of the Earth. The shape of the orbit is circular and the mass of the space shuttle is 6.8*104kg. The mass of the Earth is 6.0*1024kg and the radius of the Earth is 6.4 *106m. Calculate the energy needed to put the space shuttle into orbit.


Homework Equations



KE=GMm/rp

The Attempt at a Solution


Using G=6.67*10-11 with the mass of the Earth and shuttle and the radius of the Earth gives 4.2*1012J but the answer should be 2.2*1012J according to the book. Where am I going wrong?
 
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  • #2
Think about what the gravitational potential energy GMm/r means.

The shuttle lifts (or rises) from re to re+300 km, where re is the radius of the earth.
 
  • #3
oops!

Hi calculator20! :smile:
calculator20 said:
The space shuttle orbits about 300km above the surface of the Earth. The shape of the orbit is circular and the mass of the space shuttle is 6.8*104kg. The mass of the Earth is 6.0*1024kg and the radius of the Earth is 6.4 *106m. Calculate the energy needed to put the space shuttle into orbit.
…
KE=GMm/rp

erm :redface: … you can't just leave it there :rolleyes: … it'll crash! :eek:

try giving it a shove! :smile:​
 
  • #4
If I do GMm/re I get 4.2*10 to the 12, GMm/re + 300000 gives 4.06 * 10 to the 12. The difference between them isn't 2.2 *10 to the 12?
I get
 
  • #5
i am having exactly the same difficulty, its frustrating the hell out of me.
either i am not seeing something or there is an error in the answer page
 
  • #6
yesyesyes said:
i am having exactly the same difficulty, its frustrating the hell out of me.
either i am not seeing something or there is an error in the answer page

Welcome to PF.

They want the total energy.

What is total energy to move from the surface of Terra to a 300km height?

What must the object have to be in orbit?

Etotal = ΔKE + ΔPE
 
  • #7
so basically 2.2= KE (4.2) - PE (2.1)
allowing for roundings
?

Thanks a lot x
 

1. What type of energy is used to put a space shuttle in orbit?

The main type of energy used to put a space shuttle in orbit is chemical energy. This is stored in the rocket's fuel and is converted into kinetic energy as the rocket launches off the launch pad.

2. How much energy is needed to put a space shuttle in orbit?

The amount of energy needed to put a space shuttle in orbit varies depending on the size and weight of the shuttle, as well as the altitude and speed of the orbit. On average, it takes about 3.2 million pounds of fuel to put a space shuttle into orbit.

3. How is energy conserved during the process of putting a space shuttle in orbit?

Energy is conserved during the process of putting a space shuttle in orbit through the use of multi-stage rockets. These rockets are designed to drop off once their fuel is depleted, reducing the weight of the shuttle and conserving energy for the next stage of the launch.

4. Is renewable energy used to put a space shuttle in orbit?

No, renewable energy is not currently used to put a space shuttle in orbit. The amount of energy needed for such a launch is too large for current renewable energy technology to handle. However, renewable energy sources are being researched and developed for future space missions.

5. How does gravity affect the energy needed to put a space shuttle in orbit?

Gravity plays a significant role in the energy needed to put a space shuttle in orbit. The Earth's gravity pulls the shuttle towards its center, requiring a large amount of energy to overcome this force and achieve the necessary velocity to enter orbit. This is why rockets are designed to use the Earth's rotation to their advantage, launching from east to west to take advantage of the Earth's spin and reduce the amount of energy needed.

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